On Thu, 25 May 2006, Robert Kern apparently wrote:
What continuity? This is floating-point arithmetic.
Sure, but a continuity argument suggests (in the absence of specific floating point reasons to doubt it) that a better approximation at one point will mean better approximations nearby. E.g.,
epsilon = 0.00001 sin(100*pi+epsilon)
Compare to the bc result of 9.9999999998333333e-006
bc 1.05 Copyright 1991, 1992, 1993, 1994, 1997, 1998 Free Software Foundation, Inc. This is free software with ABSOLUTELY NO WARRANTY. For details type `warranty'. scale = 50 epsilon = 0.00001 s(100*pi + epsilon) .00000999999999983333333333416666666666468253968254